SOLUTION: X^1/2-3x^1/4+2=0

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Question 1037741: X^1/2-3x^1/4+2=0
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E2=x%5E%281%2F2%29x%5E%281%2F2%29=x%5E%281%2F4%29------this might not display well on the page...


p%5E2-3p%2B2=0

%28p-1%29%28p-2%29=0

system%28p=1%2Cor%2Cp=2%29


system%28x%5E%281%2F2%29=1%2Cor%2Cx%5E%281%2F2%29=2%29
raise each side to the half power.

x=1 or x=4

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
X^1/2-3x^1/4+2=0.
~~~~~~~~~~~~~~~~~ 

Introduce a new unknown p = x%5E%281%2F4%29.
Then x%5E%281%2F2%29 = p%5E2, and your equation takes the form

p%5E2+-+3p+%2B+2 = 0.

Factor left side. You will get

(p-1)*(p-2) = 0.

The roots are p=1  or/and  p=2.

Since p = x%5E%281%2F4%29, it means that  

x%5E%281%2F4%29 = 1     (1)

or/and  

x%5E%281%2F4%29 = 2.    (2)

Raise 1) and (2) into degree 4. you will get the solutions of the original problem

x = 1  or/and  x = 2%5E4 = 16.

Answer.  x = 1  or/and  x = 16.


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

X^1/2-3x^1/4+2=0
matrix%281%2C1%2C+x%5E%281%2F2%29+-+3x%5E%281%2F4%29+%2B+2+=+0%29%5E%22%22___________